Author Unknown

It is the responsibility of the teacher to actively involve his or her students in the learning process. The most important thing he or she should do is to avoid giving clear, concise, organized lectures. If the presentation of a lesson is too easy to follow, most of the class will not need to learn the new material on their own. They will have a certain degree of confidence in their new knowledge, and this will tend to stifle their intellectual pursuits. If, on the other hand, the lecture is vague, rambling and disorganized, the students will leave with their heads full of questions. In fact, they will be so filled with curiosity that they will try to expand their knowledge on their own.
There are many ways to present a thought provoking lecture. One of the easiest techniques to use is a foreign accent. If the accent is thick enough, even a well organized lecture will produce expressions of intellectual wonder among the students. Effective accents can be acquired in Alabama, China, India, Latin America, New York City, Germany, or any foreign country.
For natives of Kansas, that is, for individuals who cannot speak anything but perfect Midwestern English, this technique may offer difficulties. There are two possible solutions:

After a couple of sentences, most of the class will be staring at their watches or out the windows. Very quickly, they will become very anxious to go out and learn the material on their own.
In addition, to being aware of one's own speech patterns, the teacher should also pay close attention to the written word. Effective use of the black board should be considered almost a necessity. Illegible handwriting can stimulate a student's interest in new material almost as effectively as incoherent lectures. Often students will meet outside of class to exchange interpretations of lecture notes. Thus illegible handwriting encourages students to work together and share ideas.
Writing illegibly requires a great deal of practice to be effective. If one does not have satisfactory handwriting (that is to say, if one's handwriting is suitable only for formal invitations and eye charts), certain "tricks" can be learned: There is one last point on teaching technique. It is important that one does not overprepare for lectures. Generally, one should arrive at class a few minutes early, open the book, and glance at the topic for that particular day. Lectures prepared in this manner have a certain freshness and spontaneity that is often mission from those which are more carefully organized. In addition, students will gain a greater appreciation for a correct proof is they see how much time can be spent on a wrong approach.
The first section of this guide has dealt with actual teaching, concentrating on lecturing "tricks", techniques, and preparation. The subject of the last part will be general appearances.
Students tend to have more confidence in an instructor if they believe he or she has a thorough understanding of his or her field. To show a class that one has a thorough understanding of mathematics, it is necessary to appear "spaced-out." Being "spaced-out" implies one is so involved with abstract mathematics that one has lost touch with the real world. There are several ways to project such an image. By being properly "spaced-out", one will gain the confidence and respect of one's students. This will make it easier to help inspire them in their study of mathematics. Being properly "spaced-out" will also help one to acquire tenure at this or any other reputable college or university.